THE ORIGIN OF METALS IN THE CIRCUM-GALACTIC MEDIUM OF ...

submitted to the ApJ Preprint typeset using LATEX style emulateapj v. 5/2/11

THE ORIGIN OF METALS IN THE CIRCUM-GALACTIC MEDIUM OF MASSIVE GALAXIES AT Z = 3 Sijing Shen1 , Piero Madau1,2 , Anthony Aguirre 1 , Javiera Guedes1,3 , Lucio Mayer4 , and James Wadsley5

arXiv:1109.3713v1 [astro-ph.CO] 16 Sep 2011

submitted to the ApJ

ABSTRACT We present a detailed study of the metal-enriched circum-galactic medium of a massive galaxy at z = 3 using results from the “Eris” suite of new cosmological hydrodynamic “zoom-in” simulations in which a close analog of a Milky Way disk galaxy arises at the present epoch. The reference run adopts a blastwave scheme for supernova feedback that generates galactic outflows without explicit wind particles, a star formation recipe based on a high gas density threshold, and metal-dependent radiative cooling. Eris main progenitor at z = 3 resembles a “Lyman break” galaxy of total mass Mvir = 2.4 × 1011 M⊙ , virial radius Rvir = 48 kpc, and star formation rate 18 M⊙ yr−1 , and its metalenriched circum-galactic medium extends as far as 200 (physical) kpc from its center. Approximately 41%, 9%, and 50% of all gas-phase metals at z = 3 are locked in a hot (T > 3 × 105 K), warm (3 × 105 K > T > 3 × 104 K), and cold (T < 3 × 104 K) medium, respectively. We identify three sources of heavy elements: 1) the main host, responsible for 60% of all the metals found within 3Rvir ; 2) its satellite progenitors, which shed their metals before and during infall, and are responsible for 28% of all the metals within 3Rvir , and for only 5% of those beyond 3Rvir ; and its satellite dwarf companions, which give origin to 12% of all the metals within 3Rvir and 95% of those beyond 3Rvir . Late (z < 5) galactic “superwinds” – the result of recent star formation in Eris – account for only < 9% of all the metals observed beyond 2Rvir , the bulk having been released at redshifts 5 < ∼ z ∼ 8 by early star formation and outflows. In the IGM, lower overdensities are typically enriched by ‘older’, colder metals. Heavy elements are accreted onto Eris along filaments via low-metallicity cold inflows, and are ejected hot via galactic outflows at a few hundred km s−1 . The outflow mass-loading factor as a function of redshift ranges between 0.1 and 1.2, and shows no correlation with the mass of the 11 host over the interval 5.0 × 109 M⊙ < ∼ Mvir < ∼ 2.4 × 10 M⊙ . Subject headings: galaxies: evolution – galaxies: high-redshift – intergalactic medium – method: numerical 1. INTRODUCTION

Studies of the ionization, thermodynamic, and kinematic state of heavy elements in circum-galactic gas hold clues to understanding the exchange of mass, metals, and energy between galaxies and their surroundings. The distribution of observed metals in the intergalactic medium (IGM) is highly inhomogeneous, with a global cosmic abundance at z = 3 of [C/H]= −2.8 ± 0.13 for gas with overdensities 0.3 < δ < 100 (Schaye et al. 2003). The characteristic epoch of this enrichment and its main donors remain uncertain. Late supernova-driven “superwinds” from massive galaxies (e.g., Aguirre et al. 2001; Adelberger et al. 2003), early outflows from dwarf galaxies (e.g., Dekel & Silk 1986; MacLow & Ferrara 1999; Madau, Ferrara, & Rees 2001; Mori, Ferrara, & Madau 2002; Scannapieco, Ferrara, & Madau 2002; Furlanetto & Loeb 2003), quasar-driven winds (e.g., Scannapieco & Oh 2004), and the ejection of gas during the merging of protogalaxies (Gnedin 1998) are all likely to have left some chemical imprint on circum-galactic 1 Department of Astronomy and Astrophysics, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064. 2 Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, United Kingdom. 3 Institute for Astronomy, ETH Zurich, Wolgang-Pauli-Strasse 27, 8093 Zurich, Switzerland. 4 Institute of Theoretical Physics, University of Zurich, Winterthurerstrasse 190, CH-9057 Zurich, Switzerland. 5 Department of Physics and Astronomy, McMaster University, Main Street West, Hamilton L8S 4M1, Canada.

and intergalactic gas, but their relative contributions are not constrained by present data, and involve complex baryonic processes that are difficult to model. Observations clearly show that galactic-scale outflows with velocities of several hundred km s−1 are ubiquitous in massive star-forming galaxies at high redshift and in starburst galaxies in the local universe (e.g., Heckman, Lee, & Miley 1990; Pettini et al. 2001; Martin 2005; Veilleux, Cecil, & Bland-Hawthorn 2005; Weiner et al. 2009; Steidel et al. 2010). They also indicate that the metal content of the z ∼ 3 IGM is closely correlated with the positions of nearby galaxies: O VI systems are found to be strongly associated with known Lyman-break galaxies (LBGs), most detectable C IV sys11.5 tems (NCIV > cm−2 ) lie within 1 proper Mpc ∼ 10 from an LBG, and roughly one-third of all “intergalactic” 14 −2 are produced absorption lines with NCIV > ∼ 10 cm by gas that lies within ∼80 proper kpc from an LBGs (Adelberger et al. 2003, 2005). Somewhat puzzling, the comoving mass density of C IV ions in the IGM is found to drop by a factor of 4 at z > ∼ 5 (Ryan-Weber et al. 2009; Simcoe et al. 2011). Understanding the galaxy-IGM ecosystem, i.e. the role of inflows, outflows, star formation and active galactic nucleus (AGN) “feedback” in governing the gaseous and metal content of galaxies and their environment, is the goal of many recent theoretical efforts. Hydrodynamical simulations of galaxy formation over large cosmological volumes, while advancing rapidly over the

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Metals in circum-galactic medium

past few years (e.g. Cen, Nagamine, & Ostriker 2005; Oppenheimer & Davé 2008, 2009; Wiersma et al. 2009; Shen et al. 2010; Cen & Chisari 2011), typically suffer from poor spatial and mass resolution – which limits their ability to follow self-consistently the venting of metals by small galaxies and the transport of heavy elements from their production sites into the environment. And while with suitable wind prescriptions these simulations have shown that galactic outflows can potentially enrich the IGM to approximately the observed levels, it is not clear whether the same prescriptions are also able to produce realistically looking galaxies. To shed some light on the objects and processes responsible for seeding the circumgalactic and intergalactic medium with nuclear waste, we follow here a different approach. We present results from a new cosmological N -body/smooth particle hydrodynamic (SPH) suite of simulations of extreme dynamic range in which, for the first time, a close analog of a Milky Way disk galaxy has been shown to arise at z = 0 (Guedes et al. 2011). Termed “Eris”, the simulations follow the assembly of a massive galaxy halo with a total of nearly 20 million particles (gas + dark matter + stars) within the final virial radius, and a force resolution of 120 pc. The feedback from an active galactic nucleus is neglected, and a star formation recipe is adopted based on a high gas density threshold. Heating by supernovae occurs in a clustered fashion, and the resulting pressuredriven outflows at high redshifts remove low angular momentum metal-enriched gas. As shown below, our detailed study of the circum-galactic medium of Eris’ main progenitor at z = 3 reveals that late galactic superwinds – the result of recent star formation – account for only a small fraction of all the metals found between ∼ 100 and 200 (proper) kpc from the center of the main host, and resolves two other sources for the heavy elements found in Eris’ environment: its satellite progenitors – which deposit their metals before and during infall – and its orbiting dwarf companions. The paper is organized as follows. In § 2 we describe the Eris simulations. § 3 presents a detailed study of Eris’ circum-galactic medium. The origin of circum-galactic metals and the role played by satellite progenitors and companions in polluting Eris’ environment are discussed in § 4. The properties of the supernova-driven outflows from the main host are analyzed in § 5. Finally, in § 6 we summarize our main results. Throughout this work, we use the metal mass fraction Z⊙ = 0.0142 for the solar abundance (Asplund et al. 2009). 2. THE ERIS SIMULATIONS

The Eris suite of simulations was performed in a Wilkinson Microwave Anisotropy Probe 3-year cosmology running the parallel TreeSPH code Gasoline (Wadsley et al. 2004). Details of the main simulation are given in Guedes et al. (2011), and are briefly summarized here. The high-resolution region, 1 Mpc on a side at z = 0, is embedded in a low-resolution, dark matteronly, periodic box of 90 comoving Mpc on a side, and contains 13 million dark matter particles and an equal number of gas particles, for a final dark and gas particle mass of mDM = 9.8 × 104 M⊙ and mSPH = 2 × 104 M⊙ , respectively. The gravitational softening length, ǫG , was fixed to 120 physical pc for all particle species from z = 9 to the present, and evolved as 1/(1 + z) from z = 9

Fig. 1.— The optical/UV stellar properties of Eris at z = 3. The images were created with the radiative transfer code Sunrise (Jonsson 2006), and show a rest-frame B, U , and N U V stellar composite of the simulated galaxy seen face-on (top panel) and and edge-on (bottom panel). A Kroupa IMF was assumed. The 10 kpc bar in the bottom panel is in proper units.

to the starting redshift of z = 90. Compton cooling, atomic cooling, and metallicity-dependent radiative cooling at low temperatures (Mashchenko et al. 2006) are included. A uniform UV background modifies the ionization and excitation state of the gas and is implemented using a modified version of the Haardt & Madau (1996) spectrum. Star formation occurs stocastically when cold (T
108 M⊙ (424 with Ms > 107 M⊙ ), many of them also forming stars and polluting their surroundings. The total mass of heavy elements in the gas phase within Rvir , 2Rvir , and 3Rvir is 1.7 × 107 M⊙ , 2.9 × 107 M⊙ , and 3.0 × 107 M⊙ , respectively. A region ∼ 100 kpc in size is enriched to metallicities above 0.03 solar. The extent of the metal enriched region is consistent with recent observations of circum-galactic metals around LBGs (Steidel et al. 2010). Figure 3 shows a projected gas metallicity and velocity map in a 500 × 500 × 10 kpc3 slice. The arrows indicate the direction and magnitude of the mass-

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Fig. 4.— Distribution of all enriched gas in the temperaturedensity plane at z = 3 within the simulated volume. The color scale indicates the mass-weighted metallicity.

weighted peculiar velocity field relative to the center of Eris. Galactic winds can be clearly seen propagating perpendicularly to the disk (seen edge-on in this projection) well beyond the virial radius, with average velocities (over the slice) that exceed 250 km s−1 (we shall see below that individual gas particle speeds can reach 800 km s−1 ). The outflows have a bipolar distribution with a smaller opening angle near the base, similar to the observed morphologies of galactic winds in star-forming galaxies (Veilleux, Cecil, & Bland-Hawthorn 2005). Inflows along large-scale filaments bring in both pristine gas (gray arrows in the figure), as well as material preenriched by dwarf satellite companions (colored arrows on the left side of the figure and in the inset). It is instructive at this stage to look at the massweighted distribution of all (inside and outside the main host) enriched gas at z = 3 in the temperature-density plane. Figure 4 indicates that metals are spread over a large range of phases, from cold star-forming material at T < 3 × 104 K and n > nSF = 5 atoms cm−3 (corresponding to δ ≡ ρ/ρmean > 3 × 105 at z = 3) to hot T > 106 K low density δ = 3 intergalactic gas that cannot cool radiatively over a Hubble time. The black strip in the lower left corner of the figure marks the pristine, adiabatically cooling IGM, while the colored swath in the lower right corner shows dense, metal-rich gas in the galaxy disk cooling down below 104 K. Hot enriched gas vented out in the halo by the cumulative effect of SN explosions can be seen cooling and raining back onto the disk in a galactic fountain. Intergalactic gas in the range 1< ∼δ< ∼ 10 shows a strong positive gradient of metallicity with increasing temperature, and has the largest range of metallicities, extending from solar all the way down to zero. A census of all the gas-phase metals in the cold (T < 3 × 104 K), warm (3 × 104 K < T < 3 × 105 K), and hot

Fig. 5.— Top panel: Evolution with redshift of the mass fraction of heavy elements in the gas phase within the simulated volume. The three curves shows the metal fraction of cold (T < 3 × 104 K), warm (3 × 104 K < T < 3 × 105 K), and hot (T > 3 × 105 ) interstellar and circumgalactic gas. Bottom panel: Cumulative metal mass fraction in each gas phase at z = 3 as a function of overdensity.

(T > 3 × 105 K) interstellar and circumgalactic medium within the simulated volume is depicted in Figure 5 (top panel) as a function of redshift. The metal fraction of cold gas drops from about 70% at redshift 8 to 50% at z = 3. Hot gas is the second most important reservoir of gas-phase heavy elements, with a metal fraction that increases from 15% at z = 8 to 40% at z = 3. This phase would remain undetected in UV spectroscopic studies of high redshift galaxies, and would therefore contribute to the “missing metals” (Pettini 2006; Bouché et al. 2007). The metal mass fraction in warm gas remains around 10% at all epochs. More than 40% of all gas-phase metals at z = 3 lie outside the virial radius: while cold metal-rich material traces large overdensities within the main host, about 50% of all warm and 70% of all hot metals are found in low density δ < 30 regions beyond the virial radius, a point illustrated in the bottom panel of Figure 5. Intergalactic metals are characterized by a strong temperature gradient with overdensity, as the metal-weighted temperature climbs from 104 K at δ = 1 to 2 × 105 K at δ = 10. The metallicities of the individual cold, warm, and hot

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Fig. 6.— Mean metallicity of cold, warm, and hot gas in the simulated volume as a function of gas overdensity in four redshift bins. The thin blue line shows the total gas metallicity.

Fig. 7.— Fractional amount of metals at redshift 3 at overdensity δ(z = 3) that was added to gas particles before redshift z = 4, 5, 6.1, 6.8, 7.9.

gas components, as well as that of the total gas phase, are shown in Figure 6 as a function of gas overdensity in four redshift bins. The gas-phase metallicity distri-

bution at z = 3 shows a positive density gradient above an overdensity of log δ = 2, with little redshift evolution as heavy elements removed from high density regions are steadily replenished. The mean total metallicity exhibits a plateau around log δ = 1 − 2, where the metals transported by SN-driven winds accumulate, and drops quickly below log Z/Z⊙ = −2 at overdensities below a few. A low-density peak is more clearly seen in the metallicity distribution of cold, warm, and hot gas: in the case the warm and hot medium the peak is shifted towards underdense δ < ∼ 1 regions. At z = 3, the mean metallicity of cold gas drops quickly below log Z/Z⊙ = −2 at overdensities δ < ∼ 10. While our “zoom-in” simulation focuses on the circumgalactic medium of a single massive system and cannot describe the enrichment history of the IGM as a whole by a population of galaxies with different masses and star formation histories, it is still instructive to briefly compare our results with those of very recent, much lower resolution, large cosmological volume simulations of IGM pollution that use different sub-grid prescriptions for generating galactic outflows (Wiersma et al. 2009; Cen & Chisari 2011; Oppenheimer et al. 2011). Cen & Chisari (2011) inject thermal energy and metals from SN feedback on tens of kiloparsecs scales, do

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Fig. 8.— Projected gas metallicity map of Eris circum-galactic medium at z = 3 in a 500×300×300 kpc3 (proper) box. The galaxy center and its virial radius are indicated by the plus sign and the black circle, respectively. The color coding indicates the mean gas metallicity in a column of area dxdy = 7.1 × 4.3 kpc2 . The different panels highlight different enrichment redshift ranges. Gas enriched at earlier epochs generally lies at larger distance to the main host’s center, as galactic outflows transport metals from the dense regions of star formation into the circum-galactic medium on cosmological timescales. At galactocentric distances > 100 kpc the IGM is enriched mostly by satellites.

in the momentum-conserved wind implementation of kinetic feedback by Oppenheimer et al. (2011) (where hydrodynamic forces are temporarily turned off) there is no low-density peak in the metallicity-density relation and metals largely reside in cool gas. IGM metals reside primarily in a warm-hot component in the simulations of Wiersma et al. (2009), who also use kinetic feedback but with non-decoupled wind models. 4. THE ORIGIN OF CIRCUM-GALACTIC METALS

Fig. 9.— Gaseous metal mass in 2.5 kpc thick radial shells at varying distances from the center at z = 3. These metals were released by z = 3 from Eris’ main host (solid lines) and its satellites galaxies (dashed lines). The colors indicate metals produced at different enrichment epochs.

not turn off hydrodynamic coupling between the ejected metals and the surrounding gas, and, like in Eris, find that a large fraction of all the heavy elements in the gas phase at redshift 3 have temperatures in excess of 3 × 104 K. Their metallicity-density relation for cold gas also shows a low-density peak, albeit shifted towards underdense regions compared to Eris. For comparison,

In the absence of metal diffusion (Shen et al. 2010), the SPH technique allows us to trace back in time the enrichment history of every gas particle. In this and the following section we use simulation outputs from the ErisMC run and the Amiga’s Halo Finder (AHF, Knollmann & Knebe 2009) to identify the age of the metals observed at redshift 3 and the sources of pollution – whether dwarf satellite companions, dwarf progenitors, or the main host. Figure 7 shows the fraction of metals at redshift 3 that was released to gas particles at overdensity δ(z = 3) before redshifts z = 4, 5, 6.1, 6.8, 7.9. The epoch at which a gas element is enriched is clearly a sensitive function of its overdensity at some later time. The diffuse IGM is typically enriched earlier than high density regions, a trend that is in agreement with the results of Wiersma et al. (2010) and Oppenheimer et al. (2011). More than 50% (35%) of all z = 3 metals at the average density were synthesized before z = 5 (z = 6), while newly produced

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Fig. 10.— Metal mass in Eris’ circum-galactic medium as a function of the mean source halo mass hMen i. Each panel indicates the physical distance of the gas from the main host’s center at z = 3. Solid lines: main host plus satellites. Dashed lines: main host only. The mass bin in all panels is ∆(loghMen i) = 0.1.

metals are mostly confined to high overdensities. There are two possible causes for this “outside-in” (a term we borrow from Oppenheimer et al. 2011) enrichment of Eris’ circum-galactic medium: 1) metals released at earlier times into the high-density regions of Eris main host and transported into the IGM via galactic winds on timescales that are comparable to the age of the universe at z = 3; and 2) metals released at earlier times into the high-density regions of Eris’ dwarf satellites and shed into the surrounding intergalactic and circum-galactic medium before and/or during infall. Eris’ satellite galaxies are referred as as “satellite companions” if they are still orbiting outside Rvir at z = 3, and “satellite progenitors” if they have been accreted by the main host before redshift 3. To identify the time, location, and source of enrichment of a given gas particle, we define a metal mass-weighted redshift as in Wiersma et al. (2010): P ∆mZ,i zi , hzen i = Pi i ∆mZ,i

(4)

where ∆mZ,i is the metal mass gained by the gas P particle in an enrichment event at redshift zi ≥ 3, and i ∆mZ,i is the total metal mass of the particle at z = 3. For every enrichment event we also derive the mass of the (satellite) halo in which the gas particle resides (i.e. the particle belongs to the AMIGA group of the satellite halo), Mh,i and the distance between the gas particle and the center of Eris, di . Analogously to equation (4), we then define a metal mass-weighted source halo mass and distance from

Eris center as hMen i = and

P i ∆mZ,i Mh,i P i ∆mZ,i

P ∆mZ,i di hDen i = Pi . i ∆mZ,i

(5)

(6)

respectively. We have separated gas particles into different groups according to their hzen i and plotted in Figure 8 the projected metallicity of each group at redshift 3. Metals within Eris’ virial radius are clearly “younger”, i.e. they are characterized by an enrichment redshift hzen i between 3 and 3.5. Because of the long wind propagation time, “older” metals with hzen i between 4 and 5 are spread over 100 (physical) kpc perpendicularly to Eris’ disk. Low-metallicity gas in this enrichment redshift range can be seen as far as 200 kpc from the main host center as it is ejected from from satellite companions (see also Figs. 2 and 3). There is little material contaminated by metals at hzen i > 5 within Eris’ virial radius. Late (zen < 5) galactic “superwinds” – the result of recent star formation in Eris’ main host – are found to account for less than 9% of all the metals observed beyond 2Rvir , Figure 9 sheds light on the role played of satellites (both progenitors and companions) in contaminating Eris’ circum-galactic medium. It shows the total mass of heavy elements released by the main host and its satellites as a function of distance from Eris’center at redshift 3. About 60% of all the metals within 100 kpc of the

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Fig. 11.— Metal mass distribution at z = 3 as a function of the comoving mean enrichment distance hDen i. The dotted vertical lines and the legend in each panel mark the comoving distance interval from Eris’ center of the enriched gas under consideration at z = 3. Solid lines: main host plus satellites. Dashed lines: main host only.

center originate from the main host, and the rest from its satellites. Beyond 100 kpc, the satellites start dominating the metal budget. Both the host and the satellites contribute to the recent (z < 4) pollution of gas within the virial radius. Older metals within Rvir typically form in satellite progenitors, collect along the filaments into the main host, and are not blown away by galactic outflows. Note how, within 150 kpc or so, the distribution of metals from satellites is rather smooth and follows that from the main host, an indication that gas polluted by star formation in satellite progenitors is stirred up and well mixed with Eris’ galactic outflows. Spikes due to individual satellite companions can be seen beyond 85 kpc. It is interesting at this stage to look at the masses of the satellites that contribute to the enrichment of the circumgalactic medium. Figure 10 shows the metal-weighted mean halo mass, hMen i (defined in eq. 5), for gas at different physical distances from Eris’ center. Most of the satellites’ metals come from systems more massive than 109 M⊙ , with the peak of the distribution typically around 109.5 M⊙ . Satellites smaller than 108.5 M⊙ do not cause significant pollution as they are unable to form many stars because of feedback. Also, halos smaller than 108 M⊙ are resolved by less than 1,000 particles in our simulation, and the inability to properly resolve high density star-forming regions in these objects may result in a numerical suppression of star formation (as our recipe is based on a high gas density threshold). The right bottom panel shows how gas beyond 150 kpc is enriched only by dwarf galaxy companions. Figure 11 provides some in-

sight on the overall transport of enriched gas by showing the metal mass distribution as a function of the enrichment distance (as defined in eq. 6). We use comoving distances to highlight departures from pure Hubble flow. Most host metals are released within 50-100 comoving kpc from the center, with those found beyond the virial radius at z = 3 originating earlier from strong galactic winds launched closer to the center. Metals from satellites can have very different kinematics. Some are ejected directly into the IGM by satellite companions, other, initially deposited in the halo of the main host by infalling dwarf progenitors, become part of Eris’ galactic outflows. We find that about 40-50% of all the satellite-produced metals found in a given distance intervals at z = 3 were produced at larger distances and then transported inwards to their current location. For example, 42% of all satellite metals found at z = 3 in the range 400-600 (comoving) kpc from Eris’ center have a mean enrichment distance larger than 600 kpc. All metals found beyond 600 comoving (150 physical) kpc were ejected by satellite companions that have not been yet accreted by the host. To better grasp the kinematics of the material enriched by satellite progenitors (i.e. dwarf galaxies that have all been accreted by the main host before z = 3), we plot in Figure 12 a metal column density map of Eris’ circum-galactic environment at three different observer redshifts, zobs = 3, 4, 5. All the heavy elements shown in the figure were produced by satellite progenitors at epochs 5 ≤ z ≤ 7. All distances are comoving and the metals are separated according to their radial peculiar velocities relative to the center of the main host, vr , in inflowing

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Fig. 12.— Metal column density map of Eris’ circum-galactic environment at three different observer redshifts, zobs = 3, 4, 5. All the heavy elements shown in the figure are produced by satellite progenitors at epochs 5 ≤ z ≤ 7. The projected region has a comoving size of 2 × 1.2 × 1.2 Mpc3 and is centered on the main host. The center of the host galaxy and its virial radius are indicated by the plus sign and black circle, respectively. The color scale indicates the logarithmic of total metal mass a column dxdy = 28.6 × 17.1 kpc2 comoving, in units of M⊙ . Left panels: inflowing material. Right panels: outflowing material.

(vr < 0, left panels) and outflowing (vr > 0, right panels). The projected mass distribution is shown in the gray scale. Inflowing metals at zobs = 5 have contaminated the vicinity of their satellite hosts, and are now being accreted onto the main host along the filamentary structure. They are subsequently dispersed during the infall and tidal disruption of their satellite hosts, become entrained in the galactic wind of the main host, and are ultimately ejected in a bipolar outflow. 5. PROPERTIES OF GALACTIC OUTFLOWS

In this section, we study the properties of Eris’ galactic ouflows and compare them with the observations as well as with other galactic wind models adopted in cosmological simulations. 5.1. Outflow velocity

An example of the evolution with time of the radial velocity of polluted material is shown in Figure 13, where we have selected gas particles that were enriched for the last time in the main host at redshift 5, and that are unbound at z = 3. Gas accretes with negative peculiar velocity onto the host, is enriched and accelerated to outflow velocities of a few hundred km s−1 by blastwave feedback, and slows down as it sweeps the ISM and halo material. The peak velocity is comparable to those observed in high redshift LBGs (e,g., Adelberger et al. 2003; Veilleux, Cecil, & Bland-Hawthorn 2005; Steidel et al. 2010). It is also comparable to the velocities adopted in various kinetic feedback models (e.g., Springel & Hernquist 2003; Oppenheimer & Davé 2006; Dalla Vecchia & Schaye 2008; Wiersma et al. 2009; Choi & Nagamine 2011). After reaching a peak value,

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Fig. 13.— Evolution of the radial velocity of gas particles last enriched at redshift 5 in the main host. Peculiar and Hubble flow velocities are indicated with the black and red curves, respectively. The solid, dotted, and dashed lines show the median, 5 percentile and 95 percentile values, respectively.

the gas’ proper velocity declines rapidly, and particles are swept by the Hubble flow as they move farther from the center into the IGM. This behaviour is typical of all enriched gas particles. The rapid decline of the proper velocity is also seen in the kinetic feedback model of Dalla Vecchia & Schaye (2008), where outflowing particles are allowed to interact hydrodyamically with the ISM, and pressure forces within the disk significantly decrease the wind speed. Observations of local starburst galaxies (e.g., Schwartz & Martin 2004; Rupke et al. 2005) have shown that outflow speeds are correlated with halo masses and star formation rates, and that the correlation flattens out for SFR> 10 M⊙ yr−1 (Rupke et al. 2005). To investigate the existence of such relationship in the Eris simulation, we plot in the upper panel of Figure 14 the peak velocity of gas particles that become unbound after they are enriched in the main host, as a function of their enrichment redshift. We choose the gas peak velocity as this is close to the flow speed when the wind is launched, and is relatively unaffected by interactions between the outflow and the ISM/gaseous halo. Note that, because of the limited time resolution, we may actually underestimate the peak velocity of gas particles that reach a maximum speed and then slow down significantly within the time interval of two simulation outputs (∆t > ∼ 140 Myr). The scatter plot shows that enriched gas particles can often reach velocities in excess of 600 km s−1 , with a few of them moving as fast as ∼ 800 − 1000 km s−1 , a value that is consistent with the highest velocity material observed in LBGs at 2 < ∼z < ∼ 3 by Steidel et al. (2010). The mass and metal-weighted outflow average speed typically ranges between 200 and 400 km s−1 . From redshift 9.3 to 3.0, the total mass of the main host halo increases from 5.0 × 109 M⊙ to 2.4 × 1011 M⊙ . The mean outflow < speed increases for 5 < ∼ z ∼ 9.3 and decreases again at z < 5, so there is no obvious correlation between ∼ halo mass and outflow speed in Eris. Similarly, we find only a weak correlation between wind velocity and star formation rate.

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Fig. 14.— Peak radial velocity of gas particles that become unbound after they are enriched in the main host, as a function of their enrichment redshift. Each dot represents a gas particle. The black and blue solid lines show the mass-weighted and metalweighted average values, respectively. The colored dashed lines show the standard deviation from the mean.

Fig. 15.— Mean metallicity of inflowing (dashed lines) and outflowing (solid lines) material as a function of redshift. The average is taken over all gas particles within a thin shell of radius Rvir and thickness 0.02Rvir .

5.2. Metallicity

Figure 15 shows the metallicity of inflowing and outflowing material at Eris’ virial radius as a function of redshift. Galactic outflows are enriched to a typical metallicity in the range 0.1 − 0.2 Z⊙ since redshift ∼ 9, with little dependence on cosmic time. The mean metallicity of inflowing gas shows a more marked evolution, as it > increases by about one dex in the interval 9 > ∼ z ∼ 3.5. This is a consequence of more processed material falling back onto Eris in “galactic fountains” as well as being accreted via infalling satellites. The gas metallicity of inflowing gas at z . 5 (Z ∼ 0.01 Z⊙) is typical of the metallicity observed in Damped Lyα and Lyman-Limit systems (e.g., Wolfe et al. 2005). 5.3. Mass-loading factor

The mass loading factor characterizes the amount of material involved in a galactic outflow, and is defined as η = M˙ w /SFR, where M˙w is the rate at which mass is ejected. Observations of galac-

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Fig. 16.— Mass loading factor as a function of cosmic time or redshift. The mass flux was measured at the virial radius (black solid and dashed curves), half the virial radius (blue curves) and one fifths of the virial radius (red curves). The solid and dashed lines indicate the total mass loading factor versus the loading factor of enriched gas only.

tic outflows powered by starbursts suggest a wide range of mass loading factors, η = 0.01 − 10, with no obvious correlation with the star formation rates of their hosts (Veilleux, Cecil, & Bland-Hawthorn 2005). In low-resolution cosmological simulations, the mass loading factor is one of the input parameters (e.g., Springel & Hernquist 2003; Oppenheimer & Davé 2006; Dalla Vecchia & Schaye 2008; Choi & Nagamine 2011). Most models adopt a constant mass loading factor, except for the momentumr-driven model (Oppenheimer & Davé 2006, 2009), where it is assumed to be inversely proportional to the host galaxy velocity dispersion σ, η = σ0 /σ. In our SN-driven blastwave feedback scheme there is no specific parameter for mass loading. In this section we explore the mass loading factor in Eris and its variation with star formation and halo mass. We compute the wind mass loading at a distance r from the center as N 1 X M˙w (r) = mi vr,i ∆r i

(7)

where ∆r is the thickness of the radial shell, N is the total number of outflow gas particles in the shell, mi is the mass of particle i and vr,i its outflow radial velocity (relative to the host’s center). We have measured the mass flux at half the virial radius and at the virial radius, and divided it by the instantaneous SFR ignoring any time delay between star formation and large-scale outflow. Figure 16 shows that the mass loading factor stays between 0.1 and 1.2 at all redshifts. These values are smaller than those assumed in kinetic feedback and in momentum-driven wind models. We find no clear correlation between mass loading factor and the mass or velocity dispersion of the host galaxy. 6. SUMMARY

We have presented a detailed study of the metalenriched circum-galactic medium of a massive galaxy at z = 3 using results from the Eris suite of new cosmological hydrodynamic “zoom-in” simulations in which a

close analog of a Milky Way disk galaxy arises at the present epoch. Our approach to understanding the role of inflows, star formation feedback, and outflows in governing the gaseous and metal content of galaxies and their environment, is different to that of many recent theoretical efforts: Eris’ extreme mass and spatial resolution allows us to follow self-consistently the venting of metals by small progenitor dwarf satellites and the transport of heavy elements from their production sites into the environment. The reference run adopts a blastwave scheme for supernova feedback that generates galactic outflows without explicit wind particles, and a star formation recipe based on a high gas density threshold. We have found that Eris’ metal-enriched circumgalactic medium extends as far as 4 virial radii (about 200 physical kpc) from its center. Approximately 41%, 9%, and 50% of all gas-phase heavy elements are hot (T > 3 × 105 K), warm (3 × 105 K > T > 3 × 104 K), and cold (T < 3 × 104 K), respectively. More than 40% of all gas-phase metals lie outside the virial radius: while cold metal-rich material traces large overdensities within the main host, about 50% of all warm and 70% of all hot metals are found in low density δ < 30 regions beyond Eris’ virial radius. Intergalactic metals are characterized by a strong temperature gradient with overdensity, as the metal-weighted temperature climbs from 104 K at δ = 1 to above 2 × 105 K at δ = 10. SN-driven winds are able to transport metals to regions at δ < ∼ 10 where they accumulate, creating a peak in the cold gas metallicitydensity relation at Z/Z⊙ ≈ 0.05. The mean metallicity of cold gas drops quickly below log Z/Z⊙ = −2 at overdensities δ < ∼ 10. We have identified three sources of heavy elements in the simulated region: 1) the main host, responsible for 60% percent of all the metals found within 3Rvir , and for none of those found beyond 3Rvir ; 2) its satellite progenitors – systems accreted by the main host before redshift 3, which shed their metals before and during infall and are responsible for 28% of all the metals within 3Rvir ; and its satellite dwarf companions – still orbiting outside the virial radius at redshift 3, which give origin to 12% of all the metals within 3Rvir and 95% of those beyond 3Rvir . Late (z < 5) galactic “superwinds” – the result of recent star formation in Eris – account for only 9% of all the metals observed beyond 2Rvir , the rest having been released at redshifts 5 < ∼z < ∼ 8. These findings confirm the ideas put forward by Porciani & Madau (2005), that “pregalactic” enrichment from dwarf satellite systems may contribute significantly to (and dominate at large distances) the pollution of the circum-galactic medium around LBGs. Substantial amounts of heavy elements are generated at a larger distance from the main host’s center than their current location, and subsequently are accreted by the host along filaments via low-metallicity cold inflows. Galactic outflows have velocities of a few hundred km s−1 . The outflows decelerate rapidly, and the resulting long metal transport timescales produce an age gradient in metals as a function of distance from the main host. The outflow mass-loading factor as a function of redshift ranges between 0.1 and 1.2, and shows no correlation with the mass of the host over the interval 11 < 5.0 × 109 M⊙ < ∼ Mvir ∼ 2.4 × 10 M⊙ .

Shen et al. 2011 As a Lagrangian particle method, SPH does not include any implicit diffusion of scalar quantities such as metals. In the absence of some implementation of diffusion, metals are locked into specific particles and their distribution may be artificially inhomogeneous (Aguirre et al. 2005; Wiersma et al. 2009). A number of simulations of even higher resolution than Eris and including a scheme for turbulent mixing that redistributes heavy elements and thermal energy between the outflow-

13

ing material and the ambient gas (a la Shen et al. 2010) are in the making. Support for this work was provided by the NSF through grant AST-0908910 (P.M.). Simulations were carried out on NASA’s Pleiades supercomputer and the UCSC Pleiades cluster. One of us (P.M.) acknowledges support from a Raymond and Beverly Sackler Visiting Fellowship at the Institute of Astronomy, Cambridge.

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